# Lesson Worksheet: Binomial Theorem: Using Partial Fractions Mathematics

In this worksheet, we will practice decomposing rational expressions into partial fractions, then expanding them using the binomial theorem.

Q1:

By decomposing into partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.

• A,.
• B, .
• C, .
• D, .
• E, .

Q2:

By decomposing into partial fractions, find the cubic approximation of and state the range of values of for which the approximation is valid.

• A,
• B,
• C,
• D,
• E,

Q3:

By expressing in partial fractions, find the cubic expansion of and state the range of values of for which the approximation is valid.

• A,
• B,
• C,
• D,
• E,

Q4:

By expressing in partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.

• A,
• B,
• C,
• D,
• E,

Q5:

By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.

• A,
• B,
• C,
• D,
• E,

Q6:

By decomposing into partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.

• A,
• B,
• C,
• D,
• E,

Q7:

By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.

• A,
• B,
• C,
• D,
• E,

Q8:

By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.

• A,
• B,
• C,
• D,
• E,

Find the percentage error in using approximation to estimate the value of , giving your answer to 2 decimal places.

Q9:

By decomposing into partial fractions, find the expansion of up to the term and state the values of for which the expansion is valid.

• A,
• B,
• C,
• D,
• E,

Find the percentage error in using approximation to estimate the value of .

Q10:

By decomposing into partial fractions, find the expansion of up to the term and state the values of for which the expansion is valid.

• A,
• B,
• C,
• D,
• E,

Find the percentage error in using the approximation to estimate the value of , giving your answer to one decimal place.